PLUG A PROGRAM FOR THE ANALYSIS OF PLUG-FLOW REACTORS WITH GAS-PHASE AND SURFACE CHEMISTRY. Reaction Design

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1 PLU CHEMKIN Collection Release 3.6 September 2000 PLUG A PROGRAM FOR THE ANALYSIS OF PLUG-FLOW REACTORS WITH GAS-PHASE AND SURFACE CHEMISTRY Reaction Design

2 Licensing: For licensing information, please contact Reaction Design. (858) (USA) or Technical Support: Reaction Design provides an allotment of technical support to its Licensees free of charge. To request technical support, please include your license number along with input or output files, and any error messages pertaining to your question or problem. Requests may be directed in the following manner: Fax: (858) , Phone: (858) Technical support may also be purchased. Please contact Reaction Design for the technical support hourly rates at or (858) (USA). Copyright: Copyright 2000 Reaction Design. All rights reserved. No part of this book may be reproduced in any form or by any means without express written permission from Reaction Design. Trademark: AURORA, CHEMKIN, The CHEMKIN Collection, CONP, CRESLAF, EQUIL, Equilib, OPPDIF, PLUG, PREMIX, Reaction Design, SENKIN, SHOCK, SPIN, SURFACE CHEMKIN, SURFTHERM, TRANSPORT, TWOPNT are all trademarks of Reaction Design or Sandia National Laboratories. Limitation of Warranty: The software is provided as is by Reaction Design, without warranty of any kind including without limitation, any warranty against infringement of third party property rights, fitness or merchantability, or fitness for a particular purpose, even if Reaction Design has been informed of such purpose. Furthermore, Reaction Design does not warrant, guarantee, or make any representations regarding the use or the results of the use, of the software or documentation in terms of correctness, accuracy, reliability or otherwise. No agent of Reaction Design is authorized to alter or exceed the warranty obligations of Reaction Design as set forth herein. Any liability of Reaction Design, its officers, agents or employees with respect to the software or the performance thereof under any warranty, contract, negligence, strict liability, vicarious liability or other theory will be limited exclusively to product replacement or, if replacement is inadequate as a remedy or in Reaction Design s opinion impractical, to a credit of amounts paid to Reaction Design for the license of the software. Literature Citation for PLUG LUG: The PLUG program is part of the CHEMKIN Collection. R. J. Kee, F. M. Rupley, J. A. Miller, M. E. Coltrin, J. F. Grcar, E. Meeks, H. K. Moffat, A. E. Lutz, G. Dixon- Lewis, M. D. Smooke, J. Warnatz, G. H. Evans, R. S. Larson, R. E. Mitchell, L. R. Petzold, W. C. Reynolds, M. Caracotsios, W. E. Stewart, P. Glarborg, C. Wang, and O. Adigun, CHEMKIN Collection, Release 3.6, Reaction Design, Inc., San Diego, CA (2000). Acknowledgements: This document is based on the Sandia National Laboratories Report SAND , authored by Richard S. Larson. 1 Reaction Design cautions that some of the material in this manual may be out of date. Updates will be available periodically on Reaction Design's web site. In addition, on-line help is available on the program CD. Sample problem files can also be found on the CD and on our web site at 2

3 PLU PLUG: A PROGRAM FOR THE ANALYSIS ALYSIS OF PLUG-FLOW REACTORS WITH GAS-PHASE AND SURFACE CHEMISTRY ABSTRACT PLUG simulates the behavior of plug-flow chemical reactors. More specifically, the program is designed to model the non-dispersive, one-dimensional flow of a chemically reacting, ideal-gas mixture in a conduit of essentially arbitrary geometry. The program makes use of the CHEMKIN and SURFACE CHEMKIN Utility packages to handle gas-phase and heterogeneous kinetics, as well as species thermodynamic properties. PLUG solves the set of differential/algebraic equations describing the reactor using the implicit numerical software DASSL the set of differential/algebraic equations describing the reactor. These equations are briefly presented here, followed by the procedures for running PLUG. A sample problem includes input and output files for flow in a circular channel, including chemical vapor deposition on the channel walls. 3

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5 CONTENTS Page LIST OF FIGURES INTRODUCTION REACTOR EQUATIONS PROGRAM STRUCTURE Optional User Programming The Save File PROGRAM INPUT Keyword Descriptions Reactor Dimensions Reactor Type Process Parameters Functional Variations with Distance Solution Control Parameters POST PROCESSING CHEMKIN Graphical Post-processor Configurable Command-line Post-processor SAMPLE PROBLEM CHEMKIN Input File for Sample Problem CHEMKIN Output File for Sample Problem SURFACE CHEMKIN Input File for Sample Problem SURFACE CHEMKIN Output File for Sample Problem PLUG Input File for Sample Problem PLUG Output File for Sample Problem REFERENCES

6 LIST OF FIGURES Figure 1. Relationship of PLUG to the CHEMKIN and SURFACE CHEMKIN pre-processors, and the associated input and output files

7 1. INTRODUCTION Tubular flow reactors have long been used throughout the chemical process industries. The tube flow configuration is a natural choice for processes that are carried out in a continuous fashion. For this reason, such reactors are usually operated at steady state. Traditional applications have included both homogeneous reactions (carried out in an empty tube) and fluid-solid heterogeneous reactions in packed beds. More recently, tubular reactors have been used extensively to deposit thin solid films via chemical vapor deposition (CVD). While this is technically a batch process with regard to the solid deposit, the reactor still operates essentially at steady state for extended periods of time. PLUG is a general model for the steady-state tube flow reactor that can be used for process design, optimization, and control. Because the general equations for chemically reacting flow involve transport phenomena in addition to kinetics and thermodynamics, rigorous reactor models are by necessity multidimensional. However, there are often practical as well as mathematical reasons for considering idealized models of reduced dimensionality. In the case of tube flow, the accepted ideal is the plug-flow reactor, in which it is assumed that there is no mixing in the axial (flow) direction but perfect mixing in the direction(s) transverse to this. It can be shown 2 that the absence of axial mixing allows the achievable reactant conversion to be maximized. Likewise, the lack of transverse gradients implies that mass-transfer limitations are absent, once again enhancing the reactor performance. Along with these practical advantages, the plug flow reactor is computationally efficient since it is modeled using first-order ordinary differential equations (ODE s), and no transport properties are needed. The CHEMKIN Application PLUG can be used to analyze plug flow reactors for arbitrary applications involving gases. Like other CHEMKIN Applications, such as SPIN, CRESLAF, and AURORA, it is designed to handle any user-specified gas-phase and surface reaction mechanisms by interfacing with the CHEMKIN and SURFACE CHEMKIN Utility software. PLUG solves the differential/algebraic system of equations using the implicit solver DASSL 3. Process parameters and solution control options are supplied to the program via Keyword input, and both text and binary solution output files are produced. In Chapter 2, governing equations for the plug flow reactor are first summarized for reference. Chapter 3 discusses the mechanics of actually running the program and pre-processors and then Chapter 4 discusses the keyword input used in specifying the problem to be solved. Chapter 5 discusses postprocessing options. Finally, Chapter 6 gives input files for a sample problem and presents a discussion of the output generated. 7

8 2. REACTOR EQUATIONS The equations governing the behavior of the plug flow reactor are simplified versions of the general relations for conservation of mass, energy, and momentum: 4 They can be derived most easily by writing balances over a differential slice in the flow direction x, with the stipulations that (a) there are no variations in the transverse direction, and (b) axial diffusion of any quantity is negligible relative to the corresponding convective term. In this way the overall mass balance (continuity equation) for the gas is found to be K g da du dρ ρ u + ρa + ua = ai g kwk. (1) dx dx dx gas Here ρ is the (mass) density and u the axial velocity of the gas, which consists of K g species; W k is the molecular weight of species k, and g k is the molar production rate of this species by all surface reactions. The quantities A and a i are the cross-sectional (flow) area and the internal surface area per unit length, respectively, of the reactor; each can be a function of x. Equation (1) simply states that the mass flow rate of the gas can change as a result of generation or consumption by surface reactions. A similar equation can be written for each species individually: dyk ρua dx K + Y a g W = W ( g a + ω A). (2) k g i gas k k k k i k Here Y k is the mass fraction of species k and ω k is its molar rate of production by homogeneous gas reactions. Such reactions cannot change the total mass of the gas, but they can alter its composition. Turning now to the energy equation, one finds ρua K g gas h k dy k dx + C p dt dx du + u + dx K g gas h Y k k 1 + u 2 2 a = a Q e K g i gas e g k a W k Kb b W i k bulk k h k (3) where h k is the specific enthalpy of species k, C p is the mean heat capacity per unit mass of the gas, T is the (absolute) gas temperature, and b k is the molar production rate of bulk solid species k by surface reactions. The distinction between bulk and surface species is discussed in the SURFACE CHEMKIN manual. Equation (3) states that the total energy (enthalpy plus kinetic) of the flowing gas changes due to the heat flux Q e from the surroundings to the outer tube wall (whose surface area per unit length is a e ) and also due to accumulation of enthalpy in the bulk solid. Equivalently, the right-hand side of Eq. (3) can be written as 8

9 i i K a Q + a g W h g i gas where Q i is the heat flux to the gas from the inner tube wall. The methods for handling Q e and Q i will be discussed below. It is worth noting that Eq. (3) does not involve the enthalpies of the surface species. k k k The momentum equation for the gas expresses the balance between pressure forces, inertia, viscous drag, and momentum added to the flow by surface reactions. Thus K g dp du df A + ρ ua + + uai g kwk = 0, (4) dx dx dx gas where P is the absolute pressure and F is the drag force exerted on the gas by the tube wall, to be discussed below. The pressure is related to the density via the ideal-gas equation of state: PW = ρrt, (5) where R is the universal gas constant and W is the mean molecular weight. b will depend, in general, on the composition of the Since the heterogeneous production rates g k and k surface as well as that of the gas, equations determining the site fractions Z k of the K s surface species are now needed. Assuming that these species are immobile, the steady-state conservation equations are extremely simple: s = 0. (6) k i.e., the net production rate of each surface species by heterogeneous reactions must be zero. There is, however, a complication. In PLUG we assume that the total site density for each surface phase is a constant. As a result, the algebraic equations represented by (6) are not all independent, and for each phase one of the equations must be replaced by the condition Z k = 1. (7) phase In order to minimize errors, Eq. (7) is used to replace Eq. (6) for the species having the largest site fraction. An analogous relation for the gas phase is not needed, since (2) is a differential (as opposed to algebraic) equation. In fact, by summing Eqs. (2) it can be shown that the Y k will automatically add up to unity at each point. The system of governing equations for the reactor is now mathematically closed. However, because the residence time τ of the gas is often a quantity of interest, it is useful to include an equation that computes it automatically. This is simply 9

10 dτ 1 =. (8) dx u Equations (1)-(8) provide a total of 5 + K g + K s differential/algebraic relations involving the dependent variables ρ, u, T, P, τ, Y k and Z k. The functions W, h, C, ω, g, s, and b can all be expressed in terms k p k k k k of these and are obtained from calls to CHEMKIN and SURFACE CHEMKIN subroutines. The quantities A(x), a i (x), and a e (x) are fixed by the reactor geometry. This then leaves only Q e, Q i, and F to be addressed. PLUG actually provides five different options for handling the reactor energy balance. First of all, the reactor can be declared to be isothermal, or the (axial) temperature profile can be specified via a subroutine; in either case Eq. (3) is not used. Alternatively, the reactor can be declared to be adiabatic (Q e = 0), or the axial heat flux profile Q e (x) can be specified. The final option is to write Q i in terms of the ambient temperature T and an overall heat-transfer coefficient U: Q i = U ( T T ). (9) Both T and U must be supplied by the user. The viscous drag force F is written in terms of a friction factor f as follows: df dx = a 1 ρu f. (10) The friction factor can in turn be expressed as a function of the local Reynolds number i 2 2 Duρ Re =, (11) µ where D is the tube diameter (or the mean hydraulic diameter for a conduit with a noncircular cross section) and µ is the gas viscosity. For laminar flow (Re < 2100) the analytical result for round tubes is 16 f =, (12) Re while for turbulent flow one can use the approximate Blasius formula, 4 f = Re (13) This approach is only approximate, especially for noncircular conduits, but viscous drag is usually of very minor importance in gas-phase reactors. In keeping with this, and in order to avoid having to calculate transport properties, the gas viscosity is computed by scaling the inlet value (supplied by the user) by (T/T in ) 0.5 and ignoring the composition dependence. 10

11 It remains to specify the initial (inlet) conditions for the reactor. Clearly, values for ρ, u, T, P, and Y k at x = 0 should be known or easily obtainable from the problem statement, the ideal gas law, and the reactor geometry, and of course τ = 0 at this point. Since there are no derivatives of the Z k in the governing equations, it might appear that no initial conditions are needed for them. However, DASSL requires that all algebraic equations be satisfied at the initial point, so Eqs. (6) and (7) must be solved for the Z k using the known values of the other variables. In PLUG this is accomplished in a separate preliminary calculation, in which DASSL is used to integrate the fictitious transient equations dz dt σ k = Γ k s k (14) in conjunction with Eq. (7) until steady state is reached. Here σ k is the site occupancy number for species k and Γ is the total site density of the phase in question. The initial values of Z k for Eqs. (14) are essentially arbitrary (unless there are multiple steady states), although better guesses will naturally lead to faster convergence. 11

12 3. PROGRAM STRUCTURE The CHEMKIN Application User Interface runs the PLUG program automatically through a mouse-driven interface and then allows the user to directly launch visualization of solution results using the CHEMKIN Graphical Post-processor. The PLUG program has a modular structure that interfaces to the CHEMKIN Utility package for obtaining kinetic, thermodynamic, and transport parameters. In addition to input directly from the user, PLUG depends on data obtained from the CHEMKIN Gas-phase and SURFACE CHEMKIN Utility packages. Therefore, to solve a reacting-flow problem the user must first execute the two preprocessor programs, chem and surf, which have access to the thermodynamic database (e.g. therm.dat ). PLUG then reads input from the user (described in Chapter 4), defines the governing equations, solves the equations, and prints solutions for the reacting-flow problem. The CHEMKIN Graphical Post-processor can then be launched from the Application User Interface to plot solution data. Figure 1 shows the relationships between these components. For more information about the CHEMKIN Application User Interface or Graphical Post-processor, please see the CHEMKIN Getting Started manual. The first step is to execute the CHEMKIN Interpreter, chem. The CHEMKIN Interpreter first reads usersupplied information about the species and chemical reactions for a particular reaction mechanism. It then extracts further information about the species thermodynamic properties from a database (e.g. therm.dat ). The user may also optionally input thermodynamic property data directly in the input file to the CHEMKIN Interpreter to override or supplement the database information. The information from the user input and the thermodynamic properties is stored in the CHEMKIN Linking File, chem.asc ; a file that is needed by the SURFACE CHEMKIN Interpreter, and later by the CHEMKIN subroutine library, which will be accessed by the PLUG program. The CHEMKIN Interpreter also writes text output (e.g. chem.out ) that includes a formatted display of the user input and diagnostic messages from the Interpreter. The SURFACE CHEMKIN Interpreter must next be executed after the CHEMKIN Interpreter has been run, because it relies on gas-phase species and element information in the CHEMKIN Linking file. The SURFACE CHEMKIN Interpreter reads user-supplied information (e.g., surf.inp ) about surface and bulk species names, surface site types, surface reactions, and optional thermochemical information. This information is written to a SURFACE CHEMKIN Linking File ( surf.asc ), and later accessed by the SURFACE CHEMKIN subroutine library when called by the PLUG program. The SURFACE CHEMKIN Interpreter also generates a text file (e.g., surf.out ) containing the input mechanism information and diagnostic messages. 12

13 Gas Phase Chemistry Gas-Phase Chemistry Thermodynamic Data CHEMKIN Interpreter Surface Processes CHEMKIN Link File Surface Reactions SURFACE CHEMKIN Interpreter SURFACE Link File CHEMKIN Library SURFACE Library PLUG Input PLUG Text Output Binary Solution File PLUG_POST Input PLUG LUG_POST Text Data Files HEMKIN Graphical Post-Processor Processor CHEMKIN Figure 1. Relationship of PLUG to the CHEMKIN and SURFACE CHEMKIN preprocessors, and the associated input and output files. Once the pre-processors have run successfully, the PLUG program can then be executed. Since the CHEMKIN and SURFACE CHEMKIN subroutine libraries must be initialized before use, the PLUG program begins by making the appropriate initialization subroutine calls. The purpose of the initialization is to read the Linking Files and to set up the internal working and storage space required by all subroutines in the libraries. 13

14 PLUG then reads the user input that defines a particular reacting flow problem and the parameters needed to solve it. This input is read in Keyword format from the input file (e.g. plug.inp ), described in Chapter 4. The program produces printed output (e.g. plug.out ) and it saves the solution in a binary Save File, save.bin. The Save File can be read by the CHEMKIN Graphical Post-processor for plotting the solution results, as discussed further in Chapter Optional User Programming In addition to using PLUG through the CHEMKIN Application User Interface, users have the flexibility to write their own interface to the reacting-flow model. To facilitate this, the PLUG program itself is written as a Fortran subroutine that may be called from a user-supplied driver routine. We provide examples of such driver routines as part of the PLUG software distribution, written in both C++ and Fortran. The driver routine performs the function of allocating total memory usage through definition of array sizes, as well as opening input and output files. PLUG checks internally to make sure that the allocated work arrays are sufficiently large to address the problem described by the input files. Programs can be linked to the PLUG subroutine by following the examples in the makefiles provided in the sample driver subdirectories ( drivers_f77 or drivers_cpp ) of the standard distribution. Users taking advantage of this flexibility should be experienced with compiling and linking program files on their operating system and must have either a C++ or Fortran compiler installed. In addition to the driver routine, the user can specify the reactor geometry with a user-written subroutine called GEOM. Similarly, the user can program the axial temperature profile with a function called TSPEC, and the external heat flux profile with a function called QE. Examples of these functions can be found in the CHEMKIN distribution, subdirectory drivers_cpp, in a file named plug_user_routines.f. Before attempting to write these custom subroutines, the user should first consider the optional Keyword input described in Section 4.5, which provides the same flexibility but without the requirement of programming and re-compiling code. 3.2 The Save File In addition to printed output, PLUG produces a binary solution file ( save.bin ) that contains the solution data. This file provides the ability to post-process the solution, using the CHEMKIN Graphical Postprocessor or an alternative program. Further information on this subject will be found in the postprocessing discussion in Chapter 5. 14

15 4. PROGRAM INPUT 4.1 Keyword Descriptions Before running PLUG, the user must prepare three separate input files: one for CHEMKIN, one for SURFACE CHEMKIN, and one for PLUG itself. The first two are described in the respective user s manuals, so attention will be focused here on the third, which enables the user to specify the process parameters for a particular simulation. The file also contains some solution control options that should ideally have little effect on the final results, but which may allow the solution to be obtained more easily and/or accurately. Each line in the input file begins with a keyword, which may be followed by a chemical species name and/or a numerical value. The specific rules governing keyword input are as follows: 1. The first four columns in the line are reserved for the keyword, which must begin in column Any other items on the line (species name and/or numerical value) can appear anywhere in columns A species name, if required, must appear before the corresponding numerical value and be separated from it by at least one space. 4. A species name must match exactly one of the names declared in the CHEMKIN or SURFACE CHEMKIN input file. 5. A numerical value can be stated in any format (integer, fixed point, or floating point). The precision (single vs. double) is determined by the program rather than by the input format. 6. If a keyword is repeated or conflicts with another, then the one last read takes precedence. 7. The last line must contain the keyword END alone. Aside from this, the order of the lines is unimportant. A summary of the available keywords and their usage is given below. It should be emphasized that many of the keywords will not appear in a given input file, either because there are default values or because there are other (perhaps conflicting) options available. For each keyword, the short description indicates the circumstances, if any, under which it must be used. 15

16 4.2 Reactor Dimensions XSTR Inlet axial position. Units: cm Default value: 0. Example: XSTR 1.5 XEND Outlet axial position, equal to the overall reactor length if XSTR is zero. Units: cm Default value: None; this is required input. Example: XEND 10.0 DIAM Tube diameter. This is to be input only if the reactor is a round, empty tube of constant cross section (and with a negligible wall thickness if keyword QFIX or HEAT is used). Otherwise, the user-supplied subroutine GEOM must specify the reactor geometry, or keywords DPRO, AFLO, AINT, and/or AEXT can be used to describe the geometry. Units: cm Default value: None; if omitted, subroutine GEOM will be used. Example: DIAM Reactor Type ADIA Flag indicating that the reactor is adiabatic. This is the default. Default: ADIA ISO TFIX QFIX Flag indicating that the reactor is isothermal, i.e., the temperature is constant at the value specified by TEMP. Default: ADIA Flag indicating that the reactor has a user-specified axial temperature profile. In this case, the user may implement function TSPEC(X), which can be compiled with the driver routine for PLUG, or keyword TPRO to describe the profile. Any value specified with keyword TEMP would be ignored when TFIX is used. Default: ADIA; a TSPEC function will not be used. Flag indicating that the reactor has a specified external heat flux profile. In this case, the user may implement function QE(X), which can be compiled with the driver routine for PLUG, or keyword QPRO to describe the profile. Default: ADIA; a QE function will not be used. HEAT Flag indicating that the heat flux to the reactor will be calculated using a specified ambient temperature (TINF) and overall heat-transfer coefficient (BIGU). Default: ADIA; zero heat loss. 16

17 4.4 Process Parameters rs TEMP Inlet gas temperature. Units: Kelvins Default value: None; this is required input unless keyword TFIX is used. Example: TEMP 300. PRES Inlet pressure. Units: atm Default value: None; this is required input. Example: PRES 1.0 VEL Inlet velocity. Units: cm/s Default value: None; this is required input unless VDOT is specified. Example: VEL 120. VDOT Inlet volumetric flow rate. Units: cm 3 /s Default value: None; this is required input unless VEL is specified. Example: VDOT 100. MOLE Flag indicating that the input gas composition (keyword GAS) is in mole fractions. This is the default. Default: MOLE MASS Flag indicating that the input gas composition (keyword GAS) is in mass fractions. Default: MOLE GAS VIS Inlet gas-phase mole or mass fraction (see keywords MOLE and MASS) for the given species. The input values will be normalized, but their sum must still be within 0.01 of unity. Units: None Default value: 0. Example: GAS NH Viscosity of the inlet gas mixture. Units: Poise (g/cm-s) Default value: 0., i.e., viscous drag is neglected. Example: VIS 0.01 SURF Estimate (initial guess) for the inlet surface site fraction of the given species. The input values for each phase will be normalized, but their sum must still be within 0.01 of unity. Units: None Default value: 0. Example: SURF HN_SIF(S)

18 BULK Bulk phase activity for the given species (assumed constant). The input values for each phase will be normalized, but their sum must still be within 0.01 of unity. Units: None Default value: 1. Example: BULK SI(D) 1.0 TINF Ambient temperature. This will be used only if keyword HEAT is specified. Units: Kelvins Default value: 298. Example: TINF 300. BIGU Overall heat-transfer coefficient based on the internal surface area. This keyword will be ignored unless HEAT is specified. Units: erg/cm 2 -s-k Default value: None; this is required input if keyword HEAT is specified. Example: BIGU 1.0E Functional Variations with Distance DPRO Hydraulic diameter as a function of distance; input otherwise obtained from SUBROUTINE GEOM(X). Units cm, cm Default None. Example: DPRO AFLO Cross-sectional area as a function of distance; input otherwise obtained from SUBROUTINE GEOM(X). Units cm, cm 2 Default None. Example: AFLO AINT Deposition area per unit length; input otherwise obtained from SUBROUTINE GEOM(X). Units cm, cm Default None. Example: AINT AEXT External surface area per unit length; input otherwise obtained from SUBROUTINE GEOM(X). Units cm, cm Default None. Example: AEXT

19 (The following keywords pertain to the problem type specified by keyword TFIX only) TPRO Temperature as a function of distance; input otherwise obtained from SUBROUTINE TSPEC(X). Units cm, Kelvin Default None. Example: TPRO (The following keyword pertains to the problem type specified by keyword QFIX only) QPRO Heat flux as a function of distance; input otherwise obtained from SUBROUTINE QE(X). Units cm, erg/cm 2 /sec Default None. Example: QPRO Solution Control Parameters ATOL Absolute error tolerance used by DASSL. Units: None Default value: 10-8 Example: ATOL 1.0E-9 RTOL Relative error tolerance used by DASSL. Units: None Default value: 10-6 Example: RTOL 1.0E-3 DX Output distance interval. This governs the frequency of printing and has no effect on the accuracy of the solution. Units: cm Default value: 0.01 Example: DX 2.0 NNEG Flag instructing DASSL to try to constrain all components of the solution vector to be nonnegative. This is usually unnecessary, but it may help to use this keyword if negative solution components appear to be causing problems. Default: Solution is not constrained. 19

20 TSTP Initial time step for integration of the fictitious transient equations by DASSL. Steady state is assumed to be reached when there is no significant change in the surface site fractions over the course of one time step (see RCHG below). Clearly, this will be erroneous if the time step is simply too short to allow any significant reaction to take place. In this case the main reactor simulation should fail, with DASSL returning an error flag of IDID = -12. This signifies that DASSL is unable to adjust the initial derivatives so as to satisfy all of the equations at the reactor inlet, and this is a foregone conclusion if any purely algebraic equations are not already satisfied. Should this occur, the simulation should be repeated with a larger value for TSTP (or, perhaps, a smaller value for RCHG). Units: sec Default value: 1. Example: TSTP 0.1 RCHG Maximum relative change in the surface site fractions (over one time step) for which the fictitious transient equations can be considered to have converged to steady state. Caution: If this parameter is set too large relative to RTOL, then the main reactor simulation may fail with IDID = -12, as discussed above, because the algebraic equations will not appear to be satisfied at the inlet. Units: None Default value: 10-6 Example: RCHG 1.0E-3 ACHG Maximum absolute change in the surface site fractions (over one time step) for which the fictitious transient equations can be considered to have converged to steady state. The convergence test is made against the sum of the ACHG value plus the product of RCHG multiplied by the old site-fraction value. Therefore, if ACHG is set to zero (by default) then only RCHG is used to control the convergence criteria. Units: None Default value: 0 Example: ACHG 1.0E-7 PSV Pseudo-velocity for use in modifying the surface species equations for improved convergence. This pseudo-convection term is incorporated into the surface site fraction equations in order to convert algebraic equations to differential equations. The value of the PSV should be small enough such that it has no effect on the solution results, but large enough to affect the convergence behavior. If not supplied, then the unmodified equations are used. The modified equations are sometimes helpful in reaching steady-state conditions for problems with stiff surface chemistry (e.g. catalytic combustion), but should not be used if no convergence problems are encountered. A recommended value to try for PSV would be about 1/10 th of the inlet velocity, but the simulation should be repeated with smaller or larger values to make sure that it has no effect on the solution. Units: cm/s Default value: there is no pseudo convection velocity imposed at the surface. Example: PSV

21 END Flag indicating the end of the input file. This line is required, and all subsequent lines will be ignored. 21

22 5. POST PROCESSING 5.1 CHEMKIN Graphical Post-processor The CHEMKIN Graphical Post-processor provides a means for quick visualization of results from PLUG. Launched from the CHEMKIN Application User Interface, the Graphical Post-processor will automatically read in the solution date from the save.bin file in the working directory. Alternatively, the postprocessor may be launched independently and a solution file may be opened from within the Postprocessor. The user may open one or more solution files in the Post-processor and may also import external data for comparisons with the simulation results. In addition, the Graphical Post-processor can be used to export all of the solution data into comma-, tab-, or space-delimited text for further analysis with other software packages. For more information on the Graphical Post-processor, please see the CHEMKIN Getting Started manual. 5.2 Configurable Command-line Post-processor In addition to the CHEMKIN Graphical Post-processor representation of solution data, we provide the user with a FORTRAN post-processor called PLUG_POST. This program reads the binary solution file and prints selected data to text files, which can then be imported by many other graphics programs. The full source-code, plug_post.f, is provided in the CHEMKIN post_processors subdirectory. Also in this directory is a makefile script for re-building the PLUG_POST program, in case the user makes changes to the source code. In this way, the user may easily configure PLUG_POST for his or her own analysis needs. To run PLUG_POST from the command-line, you will need to do the following: 1. Open a MS-DOS Prompt (PC) or shell (UNIX). 2. Change directories to your working directory, where your save.bin solution file resides. 3. Run PLUG_POST from the command-line, specifying the full path to the CHEMKIN bin directory where the plug_post executable resides, unless this is already in your environment path variable: plug_post < plug_post.inp > plug_post.out Here, plug_post.inp is an input file that contains keywords described below. The output plug_post.out will contain diagnostics and error messages for the PLUG_POST run. PLUG_POST will also create text files containing comma-separated values. The names for these files use a suffix (extension) of.csv. 22

23 PLUG_POST uses keyword input. The available keywords are printed as a banner when the program is invoked; they are also described briefly here: PREF SPEC MOLE MASS SMIN RATE DROP HELP END Requests the text file name be prefixed by a character string. Default plug Example: PREF plug Requests species fractions for a space-delimited list of species, or ALL. Default - none Example: SPEC H2 O2 OH H2O HO2 H O Print species as mole fractions. Default - MOLE. Print species as mass fractions. Default - MOLE. Do not print species whose maximum fraction is less than SMIN. Default 0.0. Print chemical production rates for a space-delimited list of species, or ALL. Default - No production rates printed. Example: RATE OH NO Eliminate reactions where relative (percent) chemical production rates are low. Default No filtering. Example: DROP.20 Print a brief guide to keyword input. Begin post-processing. 23

24 6. SAMPLE PROBLEM This section contains the input and output files for a sample problem involving the chemical vapor deposition of silicon nitride (Si 3N 4) from SiF 4 and NH 3. Since the CHEMKIN and SURFACE CHEMKIN input and output files are described in their respective user s manuals, the following discussion will focus on the input and output specific to PLUG. The input file specifies a process in which a gas mixture with an NH 3/SiF 4 mole ratio of 6:1 is fed into a tubular reactor at a rate of 588 sccm. The inlet pressure is 2 Torr, and, because the surface kinetic data is valid only at 1713 K, the entire reactor is maintained at this temperature. The length and diameter of the reactor are 60 cm and 5.08 cm, respectively. From this information it can be shown that the axial Peclet number based on inlet conditions is about 70, while the radial Damkohler number is roughly 0.2. It follows that the plug flow assumptions are reasonably well satisfied by this process. The input file also contains initial guesses for the surface site fractions at the reactor inlet. To demonstrate the ability of PLUG to obtain a solution with a bad initial guess, these are assigned the same value of 1/6. PLUG is able to solve this problem with no apparent difficulty, and the output file shown below contains the results. First, the version numbers for PLUG, CHEMKIN, and SURFACE CHEMKIN are printed. Echoing of the keyword input follows. If any errors are detected in the PLUG input file, appropriate messages would be printed here. Next is a statement that PLUG was successful in integrating the transient equations to steady state, (despite the poor quality of the initial estimates). This yields the true surface site fractions at the inlet and allows the main reactor simulation to begin. The results of the computation are printed at intervals of 10 cm, as specified by the keyword DX. At each point there is information about the states of the gas and surface phases, the gas flow velocity, the residence time, and the bulk-phase deposition rates. Several interesting features can be noted. First, it is clear that there is very little gas-phase reaction occurring: at the reactor exit, 99.99% of the gas is comprised of SiF 4, NH 3, and HF. On the other hand, the surface processes are fairly rapid, causing SiF 4 to be severely depleted and HF to build up. The resultant net increase in the number of gas-phase molecules causes the flow velocity to rise by 17% between the inlet and the exit. Still, the overall pressure drop is a barely perceptible 0.04 Torr. Turning to the solid phases, one sees that the surface is dominated by the species HN_NH 2(S); not surprisingly, the same result has been observed in other reactor simulations. Of more practical interest is the Si 3N 4 deposition rate, which falls by a factor of 3 along the reactor. This is a direct result of the SiF 4 depletion noted above. At all points, however, the Si:N molar deposition ratio is maintained precisely at

25 6.1 CHEMKIN Input File for Sample Problem ELEMENTS H N SI F END SPECIES H2 H N2 N NH NH2 NNH N2H2 N2H3 N2H4 HF F SIF4 SIF3 SIHF3 SIF3NH2 NH3 END THERMO SI J 3/67SI G E E E E E E E E E E E E E E 01 4 SIF SI 1F 2 0 0G E E E E E E E E E E E E E E+01 4 SIF 41889SI 1F 1 0 0G E E E E E E E E E E E E E E+01 4 SIF3NH SI 1N 1F 3H 2G E E E E E E E E E E E E E E+00 4 SIHF SI 1H 1F 3 0G E E E E E E E E E E E E E E+01 4 SIF SI 1F 3 0 0G E E E E E E E E E E E E E E+01 4 SIF4 J 6/76SI 1F 4 0 0G E E E E E E E E E E E E E E 02 4 HF J 6/77H 1F 1 0 0G E E E E E E E E E E E E E E 01 4 F J 9/65F G E E E E E E E E E E E E E E 01 4 END 25

26 REACTIONS H+H+M=H2+M 0.100E ! D-L H2/0.0/ H+H+H2=H2+H E NH+N=N2+H 0.300E ! JAM NH+H=N+H E ! NH3 CST NH2+H=NH+H E NH3+H=NH2+H E ! MICHAEL NNH=N2+H 0.100E ! JAM NNH+H=N2+H E ! JAM NNH+NH2=N2+NH E ! JAM NNH+NH=N2+NH E ! JAM NH2+NH=N2H2+H 0.500E ! NH3CST NH+NH=N2+H+H 0.254E ! NH3 CST NH2+N=N2+H+H 0.720E ! PG N2H2+M=NNH+H+M 0.500E ! NH3 CST N2/2/ H2/2/ N2H2+H=NNH+H E ! NH3 CST N2H2+NH=NNH+NH E ! NH3 CST N2H2+NH2=NH3+NNH 0.100E ! NH3 CST NH2+NH2=N2H2+H E ! NH3 CST NH3+M=NH2+H+M 0.140E ! MSGK N2H3+H=NH2+NH2 1.60E ! MSGK N2H3+M=N2H2+H+M 3.50E ! MSGK N2H3+NH=NH2+N2H2 2.00E ! MSGK NH2+NH2+M=N2H4+M 3.00E ! MSGK H+N2H4=H2+N2H3 1.30E ! MSGK NH2+N2H4=NH3+N2H3 3.90E ! MSGK NH+H+M=NH2+M 2.00E ! MSGK NH2+NH2=NH3+NH 5.00E ! MSGK F+NH3=NH2+HF 4.27E ! KONDRATIEV SIF4=SIF3+F 3.00E ! PHO&MEC H+SIF4=HF+SIF3 1.00E ! PHO&MEC NH2+SIF4=SIF3NH2+F 1.00E ! GUESS NH3+SIF3=SIF3NH2+H 1.00E ! GUESS NH3+SIF3=SIHF3+NH2 1.00E ! PHO&MEC END 26

27 6.2 CHEMKIN Output File for Sample Problem CHEMKIN-III GAS-PHASE MECHANISM INTERPRETER: DOUBLE PRECISION Vers /06/18 Copyright 1995, Sandia Corporation. The U.S. Government retains a limited license in this software ELEMENTS ATOMIC CONSIDERED WEIGHT H N SI F C P H H A A R SPECIES S G MOLECULAR TEMPERATURE ELEMENT COUNT CONSIDERED E E WEIGHT LOW HIGH H N SI F H2 G H G N2 G N G NH G NH2 G NNH G N2H2 G N2H3 G N2H4 G HF G F G SIF4 G SIF3 G SIHF3 G SIF3NH2 G NH3 G (k = A T**b exp(-e/rt)) REACTIONS CONSIDERED A b E 1. H+H+M=H2+M 1.00E H2 Enhanced by 0.000E H+H+H2=H2+H2 9.20E NH+N=N2+H 3.00E NH+H=N+H2 1.00E NH2+H=NH+H2 6.92E NH3+H=NH2+H2 6.36E NNH=N2+H 1.00E NNH+H=N2+H2 1.00E NNH+NH2=N2+NH3 5.00E NNH+NH=N2+NH2 5.00E NH2+NH=N2H2+H 5.00E NH+NH=N2+H+H 2.54E NH2+N=N2+H+H 7.20E N2H2+M=NNH+H+M 5.00E N2 Enhanced by 2.000E+00 H2 Enhanced by 2.000E N2H2+H=NNH+H2 5.00E N2H2+NH=NNH+NH2 1.00E N2H2+NH2=NH3+NNH 1.00E NH2+NH2=N2H2+H2 5.00E NH3+M=NH2+H+M 1.40E

28 20. N2H3+H=NH2+NH2 1.60E N2H3+M=N2H2+H+M 3.50E N2H3+NH=NH2+N2H2 2.00E NH2+NH2+M=N2H4+M 3.00E H+N2H4=H2+N2H3 1.30E NH2+N2H4=NH3+N2H3 3.90E NH+H+M=NH2+M 2.00E NH2+NH2=NH3+NH 5.00E F+NH3=NH2+HF 4.27E SIF4=SIF3+F 3.00E H+SIF4=HF+SIF3 1.00E NH2+SIF4=SIF3NH2+F 1.00E NH3+SIF3=SIF3NH2+H 1.00E NH3+SIF3=SIHF3+NH2 1.00E NOTE: A units mole-cm-sec-k, E units cal/mole NO ERRORS FOUND ON INPUT: ASCII Vers. 1.1 CHEMKIN linkfile chem.asc written. WORKING SPACE REQUIREMENTS ARE INTEGER: 1086 REAL: 723 CHARACTER: 21 Total CPUtime (sec):

29 6.3 SURFACE CHEMKIN Input File for Sample Problem SITE/SI3N4/ SDEN/4.1683E-9/ HN_SIF(S)/2/ F3SI_NH2(S)/2/ F2SINH(S)/2/ H2NFSINH(S)/2/ HN(FSINH)2(S)/4/ HN_NH2(S)/2/ END BULK SI(D)/2.066/ BULK N(D) /1.374/ END THERMO ALL HN_SIF(S) J 3/67N 1H 1SI 1F 1S E E E E E E E E E E E E E E 01 4 HN_NH2(S) J 3/67N 2H 3SI 0F 0S E E E E E E E E E E E E E E 01 4 F3SI_NH2(S) J 3/67N 1H 2SI 1F 3S E E E E E E E E E E E E E E 01 4 F2SINH(S) J 3/67N 1H 1SI 1F 2S E E E E E E E E E E E E E E 01 4 H2NFSINH(S) J 3/67N 2H 3SI 1F 1S E E E E E E E E E E E E E E 01 4 HN(FSINH)2(S) J 3/67N 3H 3SI 2F 2S E E E E E E E E E E E E E E 01 4 SI(D) J 3/67SI S E E E E E E E E E E E E E E 01 4 N(D) J 3/67N S E E E E E E E E E E E E E E 01 4 END REACTIONS NH3 + HN_SIF(S) => HN_NH2(S) + SI(D) + HF 7.562E SIF4 + HN_NH2(S) => F3SI_NH2(S) + N(D) + HF E F3SI_NH2(S) => F2SINH(S) + HF 1.0E NH3 + F2SINH(S) => H2NFSINH(S) + HF 7.562E H2NFSINH(S) + F2SINH(S) => HN(FSINH)2(S) + HF 1.0E HN(FSINH)2(S) + F2SINH(S) => 3HN_SIF(S) + N(D) + HF 1.0E END 29

30 6.4 SURFACE CHEMKIN Output File for Sample Problem CHEMKIN-III SURFACE MECHANISM INTERPRETER: DOUBLE PRECISION Vers /06/18 Copyright 1995, Sandia Corporation. The U.S. Government retains a limited license in this software. CKLIB: CHEMKIN-III GAS-PHASE CHEMICAL KINETICS LIBRARY, DOUBLE PRECISION Vers /08/05 Copyright 1995, Sandia Corporation. The U.S. Government retains a limited license in this software SPECIES MOLECULAR ELEMENT COUNT CONSIDERED WEIGHT Density Nsites H N SI F Gas phase species: 1. H H N N NH NH NNH N2H N2H N2H HF F SIF SIF SIHF SIF3NH NH SITE: SI3N E-08 moles/cm**2 18. HN_SIF(S) F3SI_NH2(S) F2SINH(S) H2NFSINH(S) HN(FSINH)2(S) HN_NH2(S) BULK: BULK1 24. SI(D) E+01 g/cm** BULK: BULK2 25. N(D) E+01 g/cm**

31 (k = A T**b exp(-e/rt)) SURFACE REACTIONS CONSIDERED A b E 1. NH3+HN_SIF(S)=>HN_NH2(S)+SI(D)+HF 7.56E SIF4+HN_NH2(S)=>F3SI_NH2(S)+N(D)+HF 3.10E F3SI_NH2(S)=>F2SINH(S)+HF 1.00E NH3+F2SINH(S)=>H2NFSINH(S)+HF 7.56E H2NFSINH(S)+F2SINH(S) 1.00E =>HN(FSINH)2(S)+HF 6. HN(FSINH)2(S)+F2SINH(S) 1.00E =>3HN_SIF(S)+N(D)+HF NOTE: A units mole-cm-sec-k, E units cal/mole NO ERRORS FOUND ON INPUT: ASCII Version 1.1 surface linkfile surf.asc written. WORKING SPACE REQUIREMENTS ARE INTEGER: 481 REAL: 642 CHARACTER: 34 Total CPUtime (sec):